Magnetic disk device and filter coefficient setting method of the magnetic disk device

ABSTRACT

According to one embodiment, a magnetic disk device includes a controlled object, a controller which controls a motion of the controlled object, and loop shaping filters each connected in parallel to the controller. During a determination of coefficients of the loop shaping filters using a transfer function from outputs of the loop shaping filters to before an input of a disturbance affecting the controlled object, the first set of coefficients of each the loop shaping filter is determined by reflecting a frequency response of the other loop shaping filters, and the determined first sets of coefficients of the loop shaping filters are set to the loop shaping filters, respectively.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is based upon and claims the benefit of priority fromJapanese Patent Applications No. 2020-134808, filed Aug. 7, 2020; No.2021-005825, filed Jan. 18, 2021; and No. 2021-129160, filed Aug. 5,2021, the entire contents of all of which are incorporated herein byreference.

FIELD

Embodiments described herein relate generally to a magnetic disk deviceand a filter coefficient setting method of the magnetic disk device.

BACKGROUND

In a magnetic disk device, in order to improve the positioning accuracyof a magnetic head with respect to a magnetic disk, it is necessary tosuppress a vibration, etc., (a disturbance) caused by a fan of a serverrack.

Meanwhile, as one of technologies for suppressing a disturbance, atechnology of adding a loop shaping filter that suppresses an NRRO(Non-repeatable runout) disturbance to a normal feedback system isknown. Here, when a plurality of loop shaping filters are added so dealwith NRRO disturbances of plurality of vibration frequencies, the loopshaping filters mutually interfere with each other, and the positioningaccuracy of a magnetic head does not improve.

Embodiments aim to provide a magnetic disk device and a filtercoefficient setting method of the magnetic disk device capable ofsuppressing disturbances of a plurality of vibration frequencies andimproving the positioning accuracy of a magnetic head.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram showing an example of the configuration of amagnetic disk device according to an embodiment.

FIG. 2 is an illustration showing an example of a control system whichsuppresses a disturbance according to the embodiment.

FIG. 3 is an illustration showing an example of a configuration in whicha plurality of stages of filter are disposed in the control systemaccording to the embodiment.

FIG. 4 is a flowchart showing an example of the main flow of a filtercoefficient setting process according to the embodiment.

FIG. 5 is a flowchart showing an example of a parameter update processaccording to the embodiment.

FIG. 6 is an illustration showing an example of the relationship of again to a frequency according to the embodiment.

FIG. 7 is an illustration showing an example of the relationship of αand φ to a variable k according to the embodiment.

FIG. 8 is an illustration showing an example of a control system whichsuppresses disturbances according to the embodiment.

FIG. 9 is a flowchart showing an example of the main flow of a filtercoefficient setting process based on an estimated suppression targetangular frequency o according to the embodiment.

FIG. 10 is a flowchart showing an example of a modification of FIG. 9.

DETAILED DESCRIPTION

In general, according to one embodiment, there is provided a magneticdisk device comprising a controlled object, a controller which controlsa motion of the controlled object, and a plurality of loop shapingfilters each connected in parallel to the controller. During adetermination of coefficients of the loop shaping filters using atransfer function from outputs of the loop shaping filters to before aninput of a disturbance affecting the controlled object, a set ofcoefficients of each the loop shaping filter is determined by reflectinga frequency response of the other loop shaping filters, and thedetermined sets of coefficients of the loon shaping filters are set toeach the loop shaping filter, respectively.

Embodiments will he described hereinafter with reference to theaccompanying drawings. It should be noted chat the disclosure is merelyan example, and the invention is not limited by the contents describedin the following embodiments. Modifications which are easily conceivableby a person of ordinary skill in the art come within the scope of thedisclosure as a matter of course. In the drawings, in order to make thedescription clearer, the sizes, shapes and the like of the respectiveparts may be illustrated schematically with changes to the actualembodiment. In the drawings, the corresponding elements may be denotedby the same reference numbers, and the detailed descriptions thereof maybe omitted.

First Embodiment

FIG. 1 is a block diagram showing an example of the configuration of amagnetic disk device 1.

The magnetic disk device 1 is composed of a head-disk assembly (HDA) 10,a head amplifier integrated circuit (hereinafter referred to as a headamplifier IC) 16, and a system on a chip (SOC) 20.

The HDA 10 has a magnetic disk 11, a spindle motor (SPM) 12, an arm 13,and a voice coil motor (VCM) 16. The magnetic disk 11 is rotated by theSPM 12. A load beam 14 is mounted on the tip of the arm 13, and amagnetic head 15 is mounted on the tip of the load beam 14. The arm 13is driven by the VCM 16, and moves/controls the magnetic head 15 to adesignated position on the magnetic disk 11.

The magnetic head 15 is structured such that a read head element and awrite head element are mounted separately on one slider. The read headelement reads data recorded on the magnetic disk 11. The write headelement writes data to the magnetic disk 11.

The head amplifier IC 16 has a read amplifier and a write driver. Theread amplifier amplifies a read signal read by the read head element,and transmits it to the read/write (R/W) channel 22. On the other hand,the write driver transmits a write current corresponding to write dataoutput from the R/W channel 22 to the write head element.

The SOC 20 includes a microprocessor (CPU) 21, the R/W channel 22, adisk controller 23 and a positioning controller 24. The CPU 21 is themain controller of the drive, and executes servo control for positioningthe magnetic head 15 via the positioning controller 24 and dataread/write control via the head amplifier IC 16. The R/W channel 22includes a read channel for executing signal processing of read data,and a write channel for executing processing of write data. The diskcontroller 23 executes interface control for controlling data transferbetween a host system (not shown) and the R/W channel 22. It should benoted that the positioning controller 24 may be realized as hardware ormay be realized as software (firmware).

A memory 25 includes a volatile memory and a nonvolatile memory. Forexample, the memory 25 includes a buffer memory of DRAM, and a flashmemory. The nonvolatile memory of the memory 25 has a storage(illustration omitted) which stores a program, etc., necessary for theprocessing of the CPU 21, and a coefficient storage 26 which storesfilter coefficients when a filter coefficient setting process which willbe described later is executed. The filter coefficient stored in thecoefficient storage 26 will be described later. It should be noted thatthe coefficient storage 26 is not necessarily stored in the memory 25but may be stored in any storage region in the magnetic disk device 1.

Here, a technology related to a filter which suppresses an NRROdisturbance (hereinafter referred to simply as a filter) will bedescribed with reference to FIG. 2.

FIG. 2 is an illustration showing an example of a control system whichsuppresses a disturbance. As shown in FIG. 2, a filter A[z] 40 isarranged parallel to a controller C[z] 30, and the combined output isinput to a controlled object P[z] 50, and the controlled object P[z] 50is operated. By operating the controlled object P[z] 50 by reflectingthe output of the filter A[z] 40 as described above, control is executedso that the effect of a disturbance d[k] is canceled. In the magneticdisk device 1 of the present embodiment, the controller C[z] 30 and thefilter A[z] 40 are included in the positioning controller 24, and thecontrolled object P[z] 50 corresponds to the VCM 16. If the magneticdisk device is a type in which a microactuator operating the writeelement and the read element minutely is mounted on the magnetic head,not only the VCM 16 but also the microactuator may be included in thecontrolled object.

The following formula (1) is used as the filter A[z] 40.

$\begin{matrix}{{A\lbrack z\rbrack} = {\frac{\mu}{\alpha}\frac{{z^{2}\cos\;\phi} - {\eta\; z\;{\cos\left( {{\omega_{0}T} + \phi} \right)}}}{z^{2} - {2\eta\; z\;\cos\;\omega_{0}T} + \eta^{2}}}} & (1)\end{matrix}$

where T is a sampling period, and η and μ are design parameters.

In addition, α and φ in the coefficients of the filter A[z] 40 areexpressed by the following formulas (2).

$\begin{matrix}{{{{M_{u_{d}d}\lbrack z\rbrack}\mspace{11mu}\text{:=}\mspace{14mu}\frac{P\lbrack z\rbrack}{1 + {{P\lbrack z\rbrack}{C\lbrack z\rbrack}}}\mspace{14mu}\alpha} = {{M_{u_{d}d}\left\lbrack e^{j\;\omega_{0}T} \right\rbrack}}},{\phi = {\arg\left( {M_{u_{d}d}\left\lbrack e^{j\;\omega_{0}T} \right\rbrack} \right)}}} & (2)\end{matrix}$

where α and φ are parameters for matching a gain and a phase at asuppression target angular frequency ω0 of a transfer function Mudd[z]from a filter output ud[k] to before an input of a disturbance d[k] ofFIG. 2. This means that the filter is designed in consideration of achange in gain and phase occurring until the signal ud[k] output fromthe filter A[z] 40 reaches a position where the disturbance d[k] isinput so that an estimate value for suppressing the disturbance d[k]estimated from a position error signal by the filter A[z] 40 cancels thedisturbance d[z].

FIG. 3 is an illustration showing an example of a control system 200 inwhich a plurality of stages of this filter are arranged. The details ofthe control system 200 will be described later.

In this case, the filter or the following formula (3) as used.

$\begin{matrix}{{{{A_{i}\lbrack z\rbrack}\mspace{14mu}\text{:=}\mspace{14mu}\frac{\mu_{i}}{\alpha_{i}}\frac{{z^{2}\cos\;\phi_{i}} - {\eta_{i}z\;{\cos\left( {{\omega_{i}T} + \phi_{i}} \right)}}}{z^{2} - {2\eta_{i}z\;\cos\;\omega_{i}T} + \eta_{i}^{2}}},{i = 1},\ldots\;,N}{{\alpha_{i} = {{M_{u_{d}d}\left\lbrack e^{j\;\omega_{i}T} \right\rbrack}}},{\phi_{i} = {\arg\left( {M_{u_{d}d}\left\lbrack e^{j\;\omega_{i}T} \right\rbrack} \right)}}}} & (3)\end{matrix}$

However, in the configuration of the control system 200 shown in FIG. 3,when a plurality of stages of filter A1[z] to AN[a] designed based onformula (3) so that only the filter Ai[z] corresponding to the targetangular frequency ωi satisfies a gain specification of the sensitivityfunction at the target angular frequency ωi are simply added, a changein the matching gain and phase under the effect of the other filters isnot considered, and an NRRO disturbance cannot be suppressed asintended.

Therefore, in the following embodiment, when a plurality or stages offilter are disposed in the control system 200 of the controlled objectP[z] 50 (the VCM 16 in the magnetic disk device 1), the effect of eachfiler on the matching of the gain and the phase of the other filters(the frequency response of the filter) is considered so that themagnetic disk device 1 executes appropriate control for a plurality ofdisturbances, suppresses disturbances as intended by the designer, andimproves the positioning accuracy of the magnetic head 15. The methodwill be described below.

First, the configuration of the control system 200 comprising the stagesof filter will be described in detail.

FIG. 3 is an illustration showing an example of the configuration of thecontrol system 200 comprising the stages of filter. As shown in FIG. 3,the control system 200 is composed such that a plurality of filtersA1[z] 401 to AN[z] 40N are arranged parallel to the controller C[z] 30,the combined output is input to the controlled object P[z] 50, and thecontrolled object P[z] 50 is operated. When the control system 200 iscomposed in this way, even if a plurality of disturbances occur, it isstill possible to execute the positioning of the controlled object P[z]50 accurately by setting different filter coefficients to the respectivefilters A[z] to cancel the effects of the respective disturbances.

In addition, FIG. 4 is a flowchart showing an example of the main flowof the filter coefficient setting process. The process of setting thefilter coefficients to the filters A1[z] 401 to AN[z] 40N will bedescribed with reference to FIG. 4. This process is executed by the CPU21 based on the instruction of the host system, for example.

The configuration tor considering the effect of each of the filtersA1[z] 401 to An[z] 40N on the matching of the gain and the phase of theother filters, more specifically, a transfer function Muidd[z] from afilter output uid[k] of each of the filters A1[z] 401 to An[z] 40N tobefore the input of the disturbance d[k] and matching αi and φi of thegain and the phase are set as the following formulas (4).

$\begin{matrix}{{{{M_{u_{id}d}\lbrack z\rbrack}\mspace{11mu}\text{:=}\mspace{14mu}\frac{P\lbrack z\rbrack}{1 + {{P\lbrack z\rbrack}\mspace{14mu}\left( {{C\lbrack z\rbrack} + {B\lbrack z\rbrack} - {A_{i}\lbrack z\rbrack}} \right)}}},{{B\lbrack z\rbrack}\mspace{14mu}\text{:=}\mspace{14mu}{\sum\limits_{i = 1}^{N}\;{A_{i}\lbrack z\rbrack}}}}{{\alpha_{i} = {{M_{u_{id}d}\left\lbrack e^{j\;\omega_{i}T} \right\rbrack}}},{\phi_{i} = {\arg\left( {M_{u_{id}d}\left\lbrack e^{j\;\omega_{i}T} \right\rbrack} \right)}}}} & (4)\end{matrix}$

Alternatively, αi and φi may be obtained such that a gain of thesensitivity function or a gain and phase of the sensitivity function attarget angular frequency ωi when all the loop shaping filters A1[z] toAN[z] are disposed become the same as a gain and phase of thesensitivity function at target angular frequency col respectively whenthe filter Ai[z] designed based on formula (3) is disposed alone so thatonly the filter Ai[z] corresponding to the target angular frequency ωisatisfies the gain specification of the sensitivity function at theangular target angular frequency ωi.

An example of the method of obtaining αi and φi. expressed as the aboveformulas (4) will be described below using an example where the numberof stages of filter A[z] is two.

First, the above formulas (4) are transformed to the following formulas(5). Accordingly, change amounts thereof from those obtained from theabove formulas (1) to (3) can be obtained (ST101).

Note that it is assumed that fi:=exp(jωiT).

$\begin{matrix}{\mspace{76mu}{{{M_{u_{id}d}\lbrack z\rbrack} = {{M_{u_{d}d}\lbrack z\rbrack}\frac{1}{1 + {{M_{u_{d}d}\lbrack z\rbrack}\mspace{14mu}\left( {{B\lbrack z\rbrack} - {A_{i}\lbrack z\rbrack}} \right)}}}}{{\alpha_{i} = {{\overset{\sim}{\alpha}}_{i}{\Delta\alpha}_{i}}},{{\overset{\sim}{\alpha}}_{i} = {{M_{u_{d}d}\left\lbrack f_{i} \right\rbrack}}},{{\Delta\alpha}_{i} = {\frac{1}{1 + {{M_{u_{d}d}\left\lbrack f_{i} \right\rbrack}\mspace{14mu}\left( {{B\left\lbrack f_{i} \right\rbrack} - {A_{i}\left\lbrack f_{i} \right\rbrack}} \right)}}}}}{{\phi_{i} = {{\overset{\sim}{\phi}}_{i} - {\Delta\phi}_{i}}},{{\overset{\sim}{\phi}}_{i} = {\arg\left( {M_{u_{d}d}\left\lbrack f_{i} \right\rbrack} \right)}},{{\Delta\phi}_{i} = {\arg\left( {1 + {{M_{u_{d}d}\left\lbrack f_{i} \right\rbrack}\mspace{14mu}\left( {{B\left\lbrack f_{i} \right\rbrack} - {A_{i}\left\lbrack f_{i} \right\rbrack}} \right)}} \right)}}}}} & (5)\end{matrix}$

When the number of stages of filter is two, as in the following formulas(6), what are obtained are α1, α2, φ1 and φ2 (ST102), and matching gainand phase which do not reflect the effect of another filter {tilde over(α)}₂, {tilde over (α)}₂, {tilde over (ϕ)}₁, {tilde over (ϕ)}₂ are knownvalues.

$\begin{matrix}{{{{A_{1}\lbrack z\rbrack} = {\frac{\mu_{1}}{\alpha_{1}}\frac{{z^{2}\cos\;\phi_{1}} - {\eta_{1}z\;{\cos\left( {{\omega_{1}T} + \phi_{1}} \right)}}}{z^{2} - {2\eta_{1}z\;\cos\;\omega_{1}T} + \eta_{1}^{2}}}},{{A_{2}\lbrack z\rbrack} = {\frac{\mu_{2}}{\alpha_{2}}\frac{{z^{2}\cos\;\phi_{2}} - {\eta_{2}z\;{\cos\left( {{\omega_{2}T} + \phi_{2}} \right)}}}{z^{2} - {2\eta_{2}z\;\cos\;\omega_{2}T} + \eta_{2}^{2}}}}}{{\alpha_{1} = {{\overset{\sim}{\alpha}}_{1}{\Delta\alpha}_{1}}},{\alpha_{2} = {{\overset{\sim}{\alpha}}_{2}{\Delta\alpha}_{2}}},{\phi_{1} = {{\overset{\sim}{\phi}}_{1} - {\Delta\phi}_{1}}},{\phi_{2} = {{\overset{\sim}{\phi}}_{2} - {\Delta\phi}_{2}}}}{{{\Delta\alpha}_{1}\mspace{14mu}\text{:=}\mspace{14mu}{\frac{1}{1 + {{M_{u_{d}d}\left\lbrack f_{1} \right\rbrack}{A_{2}\left\lbrack f_{1} \right\rbrack}}}}},{{\Delta\alpha}_{2}\mspace{14mu}\text{:=}\mspace{14mu}{\frac{1}{1 + {{M_{u_{d}d}\left\lbrack f_{2} \right\rbrack}{A_{1}\left\lbrack f_{2} \right\rbrack}}}}}}{{{\Delta\phi}_{1}\mspace{14mu}\text{:=}\mspace{14mu}{\arg\left( {1 + {{M_{u_{d}d}\left\lbrack f_{1} \right\rbrack}{A_{2}\left\lbrack f_{1} \right\rbrack}}} \right)}},{{\Delta\phi}_{2}\mspace{14mu}\text{:=}\mspace{14mu}{\arg\left( {1 + {{M_{u_{d}d}\left\lbrack f_{2} \right\rbrack}{A_{1}\left\lbrack f_{2} \right\rbrack}}} \right)}}}} & (6)\end{matrix}$

Here, Mudd[fx]A1[f2] and mudd [f1]A2[f1] are approximated as thefollowing formulas (7) (ST103).

$\begin{matrix}{{{{{M_{u_{d}d}\left\lbrack f_{2} \right\rbrack}{A_{1}\left\lbrack f_{2} \right\rbrack}} \simeq \frac{{p_{1}\left\lbrack f_{2} \right\rbrack} + {{q_{1}\left\lbrack f_{2} \right\rbrack}{\Delta\phi}_{1}}}{{\Delta\alpha}_{1}}},{{{M_{u_{d}d}\left\lbrack f_{1} \right\rbrack}{A_{2}\left\lbrack f_{1} \right\rbrack}} \simeq \frac{{p_{2}\left\lbrack f_{1} \right\rbrack} + {{q_{2}\left\lbrack f_{1} \right\rbrack}{\Delta\phi}_{2}}}{{\Delta\alpha}_{2}}}}{{{p_{i}\lbrack x\rbrack} = {{M_{u_{d}d}\lbrack x\rbrack}\frac{\mu_{i}}{{\overset{\sim}{\alpha}}_{i}}\frac{{x^{2}\cos\;{\overset{\sim}{\phi}}_{i}} - {\eta_{i}x\;{\cos\left( {{\omega_{i}T} + {\overset{\sim}{\phi}}_{i}} \right)}}}{x^{2} - {2\eta_{i}x\;\cos\;\omega_{i}T} + \eta_{i}^{2}}}},{{q_{i}\lbrack x\rbrack} = {{M_{u_{d}d}\lbrack x\rbrack}\frac{\mu_{i}}{{\overset{\sim}{\alpha}}_{i}}\frac{{x^{2}\sin\;{\overset{\sim}{\phi}}_{i}} - {\eta_{i}x\;{\sin\left( {{\omega_{i}T} + {\overset{\sim}{\phi}}_{i}} \right)}}}{x^{2} - {2\eta_{i}x\;\cos\;\omega_{i}T} + \eta_{i}^{2}}}}}} & (7)\end{matrix}$

By using these, Δα1, Δα2, Δφ1 and Δφ2 can be approximated as thefollowing formulas (8), and Δα1, Δα2, Δφ1 and Δφ2 can thereby beobtained (ST104).

$\begin{matrix}{{{\Delta\alpha}_{1} \simeq {{{p_{2}\left\lbrack f_{1} \right\rbrack}}^{- 1}\left( {{{- {{p_{2}\left\lbrack f_{1} \right\rbrack}}^{- 2}}\left( {p_{2}\left\lbrack f_{1} \right\rbrack} \right){\Delta\alpha}_{2}} - {{{p_{2}\left\lbrack f_{1} \right\rbrack}}^{- 2}\left( {{p_{2}\left\lbrack f_{1} \right\rbrack}\overset{\_}{q_{2}\left\lbrack f_{1} \right\rbrack}} \right){\Delta\phi}_{2}} + 1} \right){\Delta\alpha}_{2}}}{{\Delta\alpha}_{2} \simeq {{{p_{1}\left\lbrack f_{2} \right\rbrack}}^{- 1}\left( {{{- {{p_{1}\left\lbrack f_{2} \right\rbrack}}^{- 2}}\left( {p_{1}\left\lbrack f_{2} \right\rbrack} \right){\Delta\alpha}_{1}} - {{{p_{1}\left\lbrack f_{2} \right\rbrack}}^{- 2}\left( {{p_{1}\left\lbrack f_{2} \right\rbrack}\overset{\_}{q_{1}\left\lbrack f_{2} \right\rbrack}} \right){\Delta\phi}_{1}} + 1} \right){\Delta\alpha}_{1}}}{{\Delta\phi}_{1} \simeq {{{- \frac{\left( {p_{2}\left\lbrack f_{1} \right\rbrack} \right)}{\left( {p_{2}\left\lbrack f_{1} \right\rbrack} \right)^{2}}}{\Delta\alpha}_{2}} + {\frac{{\left( {p_{2}\left\lbrack f_{1} \right\rbrack} \right)\left( {q_{2}\left\lbrack f_{1} \right\rbrack} \right)} - {\left( {p_{2}\left\lbrack f_{1} \right\rbrack} \right)\left( {q_{2}\left\lbrack f_{1} \right\rbrack} \right)}}{\left( {p_{2}\left\lbrack f_{1} \right\rbrack} \right)^{2}}{\Delta\phi}_{2}}}}{{\Delta\phi}_{2} \simeq {{{- \frac{\left( {p_{1}\left\lbrack f_{2} \right\rbrack} \right)}{\left( {p_{1}\left\lbrack f_{2} \right\rbrack} \right)^{2}}}{\Delta\alpha}_{2}} + {\frac{{\left( {p_{1}\left\lbrack f_{2} \right\rbrack} \right)\left( {q_{1}\left\lbrack f_{2} \right\rbrack} \right)} - {\left( {p_{1}\left\lbrack f_{2} \right\rbrack} \right)\left( {q_{1}\left\lbrack f_{2} \right\rbrack} \right)}}{\left( {p_{1}\left\lbrack f_{2} \right\rbrack} \right)^{2}}{\Delta\phi}_{1}}}}} & (8)\end{matrix}$

When these are rewritten to the following formulas (9), one solutionbecomes a formula (10) (ST105).

$\begin{matrix}{\mspace{76mu}{{v = {\left( {{m_{1}w} + {m_{2}y} + m_{3}} \right)w}}\mspace{76mu}{w = {\left( {{n_{1}v} + {n_{2}x} + n_{3}} \right)v}}\mspace{76mu}{x = {{g_{1}w} + {g_{2}y}}}\mspace{76mu}{y = {{h_{1}v} + {h_{2}x}}}}} & (9) \\{{{v = {\sqrt[3]{{- \frac{{27\mu} + {2\kappa^{3}} - {9{\kappa\lambda}}}{54}} + \sqrt{\left( \frac{{27\mu} + {2\kappa^{3}} - {9{\kappa\lambda}}}{54} \right)^{2} + \left( \frac{{3\lambda} - \kappa^{2}}{9} \right)^{3}}} + \sqrt[3]{{- \frac{{27\mu} + {2\kappa^{3}} - {9{\kappa\lambda}}}{54}} - \sqrt{\left( \frac{{27\mu} + {2\kappa^{3}} - {9{\kappa\lambda}}}{54} \right)^{2} + \left( \frac{{3\lambda} - \kappa^{2}}{9} \right)^{3}}} - {\frac{1}{3}\kappa}}}\mspace{76mu}{w = {{R\left( {{Pv} + n_{3}} \right)}v}}\mspace{76mu}{y = {Q\left( {{h_{1}v} + {g_{1}h_{2}w}} \right)}}\mspace{76mu}{x = {{\left( {1 + {g_{2}h_{2}Q}} \right)g_{1}w} + {g_{2}h_{1}{Qv}}}}\mspace{76mu}{P\mspace{14mu}\text{:=}\mspace{14mu}\left( {n_{1} + {g_{2}h_{1}n_{2}Q}} \right)}\mspace{76mu}{Q\mspace{14mu}\text{:=}\mspace{14mu}\left( {1 - {g_{2}h_{2}}} \right)^{- 1}}\mspace{76mu} R\mspace{14mu}{\text{:=}\mspace{14mu}\left\lbrack {1 - {{n_{2}\left( {1 + {g_{2}h_{2}Q}} \right)}g_{1}}} \right\rbrack}^{- 1}}{\kappa\mspace{14mu}\text{:=}\mspace{14mu}\frac{{\left( {m_{1} + {g_{1}h_{2}m_{2}Q}} \right){Rn}_{3}} + \left( {{m_{1}n_{3}R} + {h_{1}m_{2}Q} + {g_{1}h_{2}m_{2}n_{3}{QR}}} \right)}{\left( {m_{1} + {g_{1}h_{2}m_{2}Q}} \right){RP}}}\mspace{76mu}{\lambda\mspace{14mu}\text{:=}\mspace{20mu}\frac{{m_{3}{RP}} + {\left( {{m_{1}n_{3}R} + {h_{1}m_{2}Q} + {g_{1}h_{2}m_{2}n_{3}{QR}}} \right){Rn}_{3}}}{\left( {m_{1} + {g_{1}h_{2}m_{2}Q}} \right)R^{2}P^{2}}}\mspace{76mu}{\mu\mspace{14mu}\text{:=}\mspace{14mu}\frac{{m_{3}n_{3}R} - 1}{\left( {m_{1} + {g_{1}h_{2}m_{2}Q}} \right)R^{2}P^{2}}}} & (10)\end{matrix}$

Also when two stages of filter, that is, the filters A1[z] and A2[z] aredisposed in the control system 200, it is possible, by obtaining thesolution as described above, to set the filter coefficients of thefilters A1[z] and A2[z] to the coefficient storage 26 so that thefilters A1[z] and A2[z] suppress the effects of different disturbances.Therefore, also when the filters A1[z] and A2[z] are disposed, thecontrol system 200 of the magnetic disk device 1 can consider the output(effect) on the matching of the gain and the phase of another filter.Consequently, the magnetic disk device 1 can suppress NRRO disturbancesas intended by the designer, and can improve the positioning accuracy ofthe controlled object P[z] 50.

Second Embodiment

In the second embodiment, Ai[z] and B[z] are expressed as functions ofparameters as in the following formulas (11). The same configurations asthose of the first embodiment are denoted by the same reference numbers.

Ai[z] and B[z] are set as the following formulas (11).

$\begin{matrix}{{{{A_{i}\left\lbrack {z,x_{i}} \right\rbrack}\mspace{14mu}\text{:=}\mspace{14mu}\frac{\mu_{i}}{\alpha_{i}}\frac{{z^{2}\cos\;\phi_{i}} - {\eta_{i}z\;{\cos\left( {{\omega_{i}T} + \phi_{i}} \right)}}}{z^{2} - {2\eta_{i}z\;\cos\;\omega_{i}T} + \eta_{i}^{2}}},{{B\left\lbrack {z,x} \right\rbrack}\mspace{14mu}\text{:=}\mspace{14mu}{\sum\limits_{i = 1}^{N}\;{A_{i}\left\lbrack {z,x_{i}} \right\rbrack}}}}{{x\mspace{14mu}{\text{:=}\mspace{14mu}\left\lbrack {\alpha_{1}\mspace{14mu}\cdots\mspace{14mu}\alpha_{N}\mspace{14mu}\phi_{1}\mspace{14mu}\cdots\mspace{14mu}\phi_{N}} \right\rbrack}^{T}},{x_{i}\mspace{14mu}{\text{:=}\mspace{14mu}\begin{bmatrix}\alpha_{i} \\\phi_{i}\end{bmatrix}}},{{\overset{\sim}{x}}_{i}\mspace{14mu}{\text{:=}\mspace{14mu}\begin{bmatrix}{\overset{\sim}{\alpha}}_{i} \\{\overset{\sim}{\phi}}_{i}\end{bmatrix}}}}} & (11)\end{matrix}$

Then, the difference between the sensitivity function at eachsuppression target angular frequency ωi when a plurality of stages offilter are disposed, and the filter Ai[z] designed based on formula (3)is disposed alone so that only the filter Ai[z] corresponding to thetarget angular frequency ωi satisfies the gain specification of thesensitivity function at the target angular frequency ωi is set as anobjective function. This objective function is the following formula(12).

$\begin{matrix}{{g(x)}\mspace{14mu}\text{:=}\mspace{14mu}{\sum\limits_{i = 1}^{N}\;{{{P\left\lbrack f_{i} \right\rbrack}}{{{B\left\lbrack {f_{i},x} \right\rbrack} - {A_{i}\left\lbrack {f_{i},{\overset{\sim}{x}}_{i}} \right\rbrack}}}}}} & (12)\end{matrix}$

where parameters αi and φi which minimize the above formula (12) areobtained. For example, the parameters are updated until |x[k+1]−x[k]|<δis satisfied in the following formula (13).

x[k+1]=x[k]−γ∇g(x[k])   (13)

FIG. 5 is a flowchart showing an example of the parameter updateprocess. This process is executed by the CPU 21 in the presentembodiment.

As shown in FIG. 5, the CPU 21 assigns initial values to the parametersαi and φi, and sets a variable k to 1 (ST201). Next, the CPU 21 adds 1to the variable k (ST202), calculates the formula (13) (ST203),determines whether the calculation result is less than δ or not (ST204),and repeats the process from step ST202 to step ST204 until thecalculation result becomes less than 6.

Then, the CPU 21 obtains αi from the above formula (4) again using theapproximate values of the converged. parameters αi and φi. It should benoted that ηi may be updated using the following formula (14).

$\begin{matrix}{{\overset{\sim}{\mu}}_{i} = {\frac{\mu_{i}}{{\hat{\alpha}}_{i}}\alpha\; i}} & (14)\end{matrix}$

FIG. 6 is an illustration showing an example of the relationship of thegain to the frequency. In addition, FIG. 6 shows a comparison among whenno filter is used (w/o LS), when a filter of a frequency of 3 kHz isused, when a filter of a frequency of 3.5 kHz is used, when filters offrequencies of 3 kHz and 3.5 kHz are used, and when the secondembodiment is applied. As shown in the graph when the second embodimentis applied, as compared with the graph when the filters of frequenciesof 3 kHz and 3.5 kHz are used, the gain becomes as the designerintended.

Furthermore, FIG. 7 is an illustration showing an example of therelationship of α and φ to the variable k. The vertical axis shows α (3kHz, 3.5 kHz) and φ (3 kHz, 3.5 kHz), and the horizontal axis shows thevariable k. As shown in FIG. 7, α (3 kHz, 3.5 kHz) and φ (3 kHz, 3.5kHz) each are converged to a constant value as the variable k increases.

Also when the filter coefficients of the filter of the control system200 are obtained as described above and the obtained filter coefficientsare set to the coefficient storage 26, the same effects as thoseproduced in the first embodiment can be produced.

In addition, when design parameters ui, ηi and ωi are adaptivelydetermined, the value of the sensitivity function at each suppressiontarget angular frequency ωi after the design parameters ui, ηi and ωiare adapted may be stored in the memory 25, and the approximate valuesof the parameters αi and φi may be obtained again to follow theprocedure of the second embodiment.

Third Embodiment

The above-described embodiments do not deal with when the suppressiontarget angular frequency ωi changes according to the environment.Therefore, an embodiment dealing with when the suppression targetangular frequency ωi changes according to the environment will bedescribed in the present third embodiment. The change according to theenvironment is, for example, a change in the disturbance, and the sameconfigurations as those of the above-described embodiments will bedenoted by the same reference numbers, and detailed descriptions thereofwill be omitted.

FIG. 8 is an illustration showing an example of a control system 300 inwhich an estimator 60 is added to the control system 200 comprising thestages of filter using the technology of FIG. 3. The estimator 60estimates the suppression target angular frequency ωi from a positionerror e[k] and the disturbance d[k]. In addition, the estimator 60inputs the estimated suppression target angular frequency ωi to each ofthe filters A1[z] 401 to AN[z] 40N. In the present embodiment, theestimator 60 estimates the suppression target angular frequency ωi fromthe position error e[k] and the disturbance d[k]. However, the presentinvention is not limited to this. For example, a rotational vibrationsensor may be disposed in the magnetic disk device 1 so that therotation of the magnetic disk device 1 can be detected, and thesuppressing target angular frequency ωi may be determined based on thedetected rotation value.

The value of the sensitivity function gain at each suppression targetangular frequency ωi is stored in a predetermined storage beforehand.The suppression target angular frequency ωi is obtained from theposition error e[k], the disturbance d[k] or both the position errore[k] and the disturbance d[k]. When the suppression target angularfrequency ωi is changed, αi and φi also need to be changed. Therefore,after the suppression target angular frequency ωi is determined, αi andφi are adjusted as in the above-described embodiments At this time, theestimator 60 executes adjustment such that the gain at the suppressiontarget angular frequency ωi of each of the filters A1[z] 401 to AN[z]40N becomes the same between before and after the change or becomes thesame as the sensitivity function at the suppression target angularfrequency ωi stored beforehand. FIG. 9 is a flowchart showing an exampleof the main flow of the process of setting the coefficients of each ofthe filters A1[z] 401 to An[z] 40N based on the estimated suppressiontarget angular frequency ωi. This process is executed by the estimator60 in the present embodiment. In addition, FIG. 10 is a flowchartshowing a modification example of the process of FIG. 9.

First, Ai[z] and Bi[z] are expressed in a format for specifyingparameters as the following formulas (15).

$\begin{matrix}{{{{A_{i}\left\lbrack {z,x_{i}} \right\rbrack}\mspace{14mu}\text{:=}\mspace{14mu}\frac{\mu_{i}}{\alpha_{i}}\frac{{z^{2}\cos\;\phi_{i}} - {\eta_{i}z\;{\cos\left( {{\omega_{i}T} + \phi_{i}} \right)}}}{z^{2} - {2\eta_{i}z\;\cos\;\omega_{i}T} + \eta_{i}^{2}}},{{B\left\lbrack {z,x} \right\rbrack}\mspace{14mu}\text{:=}\mspace{14mu}{\sum\limits_{i = 1}^{N}\;{A_{i}\left\lbrack {z,x_{i}} \right\rbrack}}}}{{x\mspace{14mu}{\text{:=}\mspace{14mu}\left\lbrack {\alpha_{1}\mspace{14mu}\cdots\mspace{14mu}\alpha_{N}\mspace{14mu}\phi_{1}\mspace{14mu}\cdots\mspace{14mu}\phi_{N}} \right\rbrack}^{T}},{x_{i}\mspace{14mu}{\text{:=}\mspace{14mu}\begin{bmatrix}\alpha_{i} \\\phi_{i}\end{bmatrix}}}}} & (15)\end{matrix}$

As in the following formula (16), the difference between the sensitivityfunction at a suppression target frequency tilde fi before the changeand the sensitivity function at a suppression target frequency fi afterthe change is set as an objective function.

$\begin{matrix}{{h(x)}\mspace{14mu}\text{:=}\mspace{11mu}{\sum\limits_{i = 1}^{N}\;{{{{P\left\lbrack {\overset{\sim}{f}}_{i} \right\rbrack}\mspace{14mu}\left( {{C\left\lbrack {\overset{\sim}{f}}_{i} \right\rbrack} + {B\left\lbrack {{\overset{\sim}{f}}_{i},\overset{\sim}{x}} \right\rbrack}} \right)} + \Delta_{i} - {{P\left\lbrack f_{i} \right\rbrack}\mspace{14mu}\left( {{C\left\lbrack f_{i} \right\rbrack} + {B\left\lbrack {f_{i},x} \right\rbrack}} \right)}}}}} & (16)\end{matrix}$

where tilde x is a parameter before the suppression target frequencychange, and Δj is a term corresponding to a target sensitivity functiongain change indicating either stable or unstable which will be describedlater. The suppression target angular frequency ωi is determined in thisway (ST301).

Then, parameters αi and φi are adjusted (ST302). More specifically, theestimator 60 obtains parameters αi and φi which minimize the aboveformula (16). For example, the parameters are updated until|x[k+1]−x[k]|<δ is satisfied in the following formula (17).

x[k+1]=x[k]−γ∇h(x[k])   (17)

When the suppression target angular frequency changes under the effectof the disturbance, etc., the control system 300 may become unstable.Therefore, the estimator 60 determines whether it is stable or not(ST303). Here, whether it is stable or not is determined based on anindex indicating stable/unstable (for example, the integral value of thesensitivity function, the cumulative sum, or the range of the parameterfor each suppression target angular frequency obtained beforehand). Whenthe estimator 60 determines that it is not stable, that is, it isunstable (ST303, NO), the estimator 60 changes Δi and ηi (S1304). Morespecifically, the estimator 60 increases the sensitivity function gainof a suppression target angular frequency and changes parameters suchthat the index decreases. Here, the parameters are the coefficients of:each of the filters A1[z] 401 to AN[z] 40N, and the sensitivity functiongain at the suppression target angular frequency ωi before the change.When the estimator 60 determines that it is not stable as describedabove, the estimator 60 executes adjustment by changing the targetsensitivity function gain during adjustment (Δi of the above formula(16) and ηi until the control system 300 becomes stable.

It should be noted that, as shown in FIG. 10, an upper limit H(ω) of ηmay be obtained beforehand (ST401), ηi<H(2πfi) may be checked and thesuppression target angular frequency ωi may be determined (ST402), andbased on the determination of whether ηi≤H(ωi) or not (ST403), Δi and ηimay be changed (ST404), and the parameters αi and φi may be adjusted(ST405).

In the present embodiment, also when the suppression target angularfrequency ωi changes according to the environment, the magnetic diskdevice 1 can set appropriate coefficients to each of the loop shapingfilters A1[z] 401 to AN[z] 40N using the estimated suppression targetangular frequency ωi. Accordingly, the magnetic disk device 1 canimprove the positioning accuracy of the magnetic head 15.

While certain embodiments have been described, these embodiments havebeen presented by way of example only, and are not intended to limit thescope of the inventions. Indeed, the novel embodiments described hereinmay be embodied in a variety of other forms; furthermore, variousomissions, substitutions and changes in the form of the embodimentsdescribed herein may be made without departing from the spirit of theinventions. The accompanying claims and their equivalents are intendedto cover such forms or modifications as would fall within the scone andspirit of the inventions.

What is claimed is:
 1. A magnetic disk device comprising: a controlledobject; a controller which controls a motion of the controlled object;and a plurality of loop shaping filters each connected in parallel tothe controller, wherein during a determination of coefficients of theloop shaping filters using a transfer function from outputs of the loopshaping filters to before an input of a disturbance affecting thecontrolled object, a first set of coefficients of each the loop shapingfilter is determined by reflecting a frequency response of the otherloop shaping filters, and the determined first sets of coefficients ofthe loop shaping filters are set to the loop shaping filters,respectively.
 2. The magnetic disk device of claim 1, wherein thedetermination of the first sets of coefficients of the loop shapingfilters comprises a preparing unit configured to prepare each the loopshaping filter for each a suppression target frequency, a firstdetermining unit configured to determine a second set of coefficients ofeach the loop shaping filter such that a first gain of sensitivityfunction at each the suppression target frequency satisfies a gainspecification of sensitivity function at each the suppression targetfrequency when each the loop shaping filter with the second set ofcoefficients corresponding to each the suppression target frequency isused alone, and a second determining unit configured to determine thefirst set of coefficients of each the loop shaping filter such that asecond gain of sensitivity function at each the suppression targetfrequency when all the loop shaping filters with the first sets ofcoefficients are used becomes the same as the first gain of sensitivityfunction at each the suppression target frequency.
 3. The magnetic diskdevice of claim 1, wherein the determination of the first sets ofcoefficients of the loop shaping filters comprises a preparing unitconfigured to prepare each a loop shaping filter for each a suppressiontarget frequency, a first determining unit configured to determine asecond set of coefficients of each loop shaping filter such that a firstgain of sensitivity function at each the suppression target frequencysatisfies a gain specification of sensitivity function at each thesuppression target frequency when each the loop shaping filter with thesecond set of coefficients corresponding to each the suppression targetfrequency is used alone, a calculating unit configured to calculate afirst phase of sensitivity function at each the suppression targetfrequency from a phase of sensitivity function when each the loopshaping filter with the second set of coefficients corresponding to eachthe suppression target frequency is used alone, and a second determiningunit configured to determine the first set of coefficients of each theloop shaping filter such that a second gain and a second phase ofsensitivity function at each the suppression target frequency when allthe loop shaping filters with the first sets of coefficients are usedbecomes the same as the first gain and the first phase of sensitivityfunction at each the suppression target frequency.
 4. The magnetic diskdevice of claim 7, wherein the determination of the first sets ofcoefficients of loop shaping filters is obtained by approximating achange in each filter coefficients caused by an effect of the other loopshaping filters when the loop shaping filter is used alone.
 5. Themagnetic disk device of claim 2, wherein the determination of the firstsets of coefficients of loop shaping filters is obtained by updating thesets of coefficients such that a difference in the gain and phase orsensitivity function or the gain of sensitivity function of each thesuppression target frequency between when a plurality of the loopshaping filters are used in combination and when each the correspondingloop shaping filter is used alone is minimized.
 6. The magnetic diskdevice of claim 1, wherein the controlled object is a voice coil motor.7. The magnetic disk device of claim 1, wherein the controlled object isa microactuator.
 8. The magnetic disk device of claim 1, wherein thecontrolled object is a voice coil motor and a microactuator.
 9. Themagnetic disk device of claim 1, wherein during the determination of thesets of coefficients of the loop shaping filters, a suppression targetfrequency of the disturbance is estimated, and the first set ofcoefficients of each the loop shaping filter is determined based on anestimated suppression target frequency.
 10. The magnetic disk device ofclaim 9, wherein when the estimated suppression target frequency ischanged, the first set of coefficients of each the loop shaping filteris determined such that the gain of sensitivity function of thesuppression target frequency becomes the same between before and afterthe change.
 11. The magnetic disk device of claim 10, wherein based onan effect of the disturbance, when a control system in which thecontroller controls the controlled object is not stable, a parameter ischanged such that the gain of sensitivity function of the suppressiontarget frequency increases.
 12. The magnetic disk device of claim 11,wherein the parameter includes the first set of coefficients of each theloop shaping filter, and the gain of sensitivity function at thesuppression target frequency before the change.
 13. The magnetic diskdevice of claim 11, wherein whether the control system is stable or notis determined using an integral value of the sensitivity function, acumulative value, or a range of the parameter for each the suppressiontarget frequency obtained beforehand.
 14. A filter coefficients settingmethod of a magnetic disk device comprising a controlled object, acontroller which controls a motion of the controlled object, and aplurality of loop shaping filters each connected in parallel to thecontroller, the filter coefficients setting method comprising the stepsperformed by the controller included in the magnetic disk device of:determining a first set of coefficients of each the loop shaping filterby reflecting a frequency response of the other loop shaping filters,during a determination of coefficients of the loop shaping filters usinga transfer function from outputs of the loop shaping filters to beforean input of a disturbance affecting the controlled object; repeatingdetermining the first sets of coefficients for the loop shaping filters;and setting the determined first sets of coefficients of the loopshaping filters to the loop shaping filters, respectively.